Consider $x^{3}+8$. Rewrite $x^{3}+8$ as $x^{3}+2^{3}$. The sum of cubes can be factored using the rule: $a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right)$.
$$\left(x+2\right)\left(x^{2}-2x+4\right)$$
Rewrite the complete factored expression. Polynomial $x^{2}-2x+4$ is not factored since it does not have any rational roots.
